From Wikipedia:
"Morley supported abolitionism, a cause closely associated with 19th-century British Whigs and political radicals, and then the British Liberal party. He became treasurer of the fund to finance Josiah Henson, an escaped American slave who was given support in Britain. Josiah Henson later wrote Uncle Tom's Story of His Life: an Autobiography of the Rev. Josiah Henson (Mrs. Harriet Beecher Stowe's 'Uncle Tom'), from 1789 to 1876."
You'll notice nobody's been trying to throw his statue into the harbour.
The statue was moved to the Horsefair here from the corner of Baldwin Street and High Street in 1921, according to the notes on this Vaughan Collection postcard in the Bristol Archives. My guess would be that (as with quite a few other things at road junctions in Bristol, like Alderman Proctor's Fountain) it was moved out of the way as the increase in motor car traffic needed more room at the busy corner, but that is only a guess.
GPS Coordinates:
51.45692, -2.59534
Location: Old City